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A336560
Numbers k at which points A336456(k) appears multiplicative, but A051027(k) does not.
8
15, 39, 51, 60, 78, 87, 95, 111, 123, 143, 159, 183, 204, 215, 219, 222, 231, 240, 247, 267, 291, 303, 312, 323, 327, 330, 335, 339, 348, 366, 380, 399, 407, 411, 438, 444, 447, 455, 471, 494, 506, 519, 543, 559, 579, 582, 591, 624, 636, 654, 671, 687, 695, 699, 703, 714, 723, 731, 732, 767, 771, 779, 798, 803, 807
OFFSET
1,1
COMMENTS
Numbers in A336557 but not in A336547.
Note that if A051027(k) = Product_{p^e|k} A051027(p^e) then also A336456(n) = Product_{p^e|n} A336456(p^e), because A336456(n) = A335915(A051027(n)) and A335915 is fully multiplicative, thus A336547 is a subsequence of A336557.
LINKS
PROG
(PARI)
is_fun_mult_on_n(fun, n) = { my(f=factor(n)); prod(k=1, #f~, fun(f[k, 1]^f[k, 2]))==fun(n); };
A051027(n) = sigma(sigma(n));
A000265(n) = (n>>valuation(n, 2));
A335915(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265((f[k, 1]^2)-1)^f[k, 2]))); };
A336546(n) = is_fun_mult_on_n(A051027, n);
A336556(n) = is_fun_mult_on_n(A336456, n);
isA336560(n) = (A336546(n)<A336556(n));
CROSSREFS
Setwise difference of A336557 and A336547. Equally, setwise difference of A336559 and A336549. Subsequence of A336548.
Cf. also A336561.
Sequence in context: A320721 A086096 A272189 * A176257 A055131 A121051
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 25 2020
STATUS
approved